Reproductivity for a nematic liquid crystal model |
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Authors: | Blanca Climent-Ezquerra Francisco Guillén-González Marko Rojas-Medar |
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Institution: | (1) Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain;(2) Dpto. Matemática Aplicada, IMECC-UNICAMP, C.P. 6065, 13081-970 Campinas-SP, Brazil |
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Abstract: | In this paper we prove existence of weak solution with the reproductivity in time property, for a penalized PDE’s system related
to a nematic liquid crystal model.
This problem is relatively explict when time-independent Dirichlet boundary conditions are imposed for the orientation of
crystal molecules. Nevertheless, for the time-dependent case, the treatment of the problem is completely different. The verification
of a maximum principle for weak reproductive solutions is fundamental in the argument.
Finally, the relation between reproductive and periodic in time (regular) solutions will be pointed out, differenting the
2D and 3D cases. Basically, in two-dimensional domains every reproductive solution is regular and time periodic, whereas the problem
remains open for three-dimensional domains. |
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Keywords: | Primary 35Q35 Secondary 76D03 35K20 35A35 |
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